Solicitors for UK Uncut Legal Action say they wrote to HMRC to ask them to quash a tax deal with Goldman Sachs. Photograph: Chris Hondros/Getty Images

Formal legal proceedings will be issued against the Revenue and Customs (HMRC) on Thursday over allegations that it let the investment bank Goldman Sachs off paying up to £20m in outstanding tax.

The application for a judicial review, initiated by the campaign group UK Uncut Legal Action, will be lodged with the administrative court in London. The organisation has called for the government to crack down on tax avoidance by large corporations and the super-rich rather than pursue its "unnecessary austerity programme".

The action comes after UK Uncut claimed that HMRC had not been sufficiently forthcoming to the Commons public accounts committee in revealing details of the tax deal it reached with Goldman Sachs.

The legal challenge has been repeatedly delayed pending responses from the Revenue. "We feel it is now undeniably in the public interest that this judicial review goes ahead in order to reverse the alleged decision by HMRC to let Goldman Sachs off up to £20m in tax and reclaim this money for the UK taxpayer," UK Uncut said.

A number of union general secretaries and MPs are supporting the action. They include Paul Kenny of the GMB, Mark Serwotka of the PCS, Christine Blower of the NUT, the Green party MP Caroline Lucas, as well as Labour MPs John McDonnell, Diane Abbott and Katy Clark.

Richard Stein from the solicitors Leigh Day & Co, who is taking the case, said: "We wrote to the HMRC in October asking them to quash the deal and reclaim the millions unpaid in taxes from one of the world's richest banks but received no response. We chased again in November and they claimed they needed more time.

"They have now replied with what we feel is an extremely weak argument as to why this decision cannot be reversed, therefore, we will now progress this legal action and issue proceedings in the high court."

Tim Street, director of UK Uncut Legal Action said: "There is overwhelming public support from unions, NGOs, MPs and thousands of ordinary people who want to see this dodgy tax deal challenged in the courts.

"It shows the deep level of outrage that people feel over state-sanctioned tax dodging by big business, while government destroys public services that ordinary people rely on, saying that there is no money."

Street accused the government of "making a political choice to turn a blind eye" to what he views as a wider tax issue that costs the public purse £25bn a year and of "slashing public services and the support for the poorest instead of clamping down".

The HMRC has disputed the figure of £20m and said there was no "systematic failure" in its dealing with Goldman Sachs.